LOGIC EQUIVALENCE IN DISCRETE MATHEMATICS , MATHEMATICS

Discrete Mathematics is a core course in mathematics and computer science that deals with structures that are fundamentally discrete rather than continuous. It provides essential tools for reasoning, problem-solving, and theoretical foundations in computing and information sciences. Course Objectives: Understand the fundamental concepts of logic, set theory, and functions. Learn techniques of mathematical reasoning and proof methods. Explore combinatorics, graph theory, and algorithms. Study relations, recurrence relations, and number theory. Apply discrete mathematical concepts to computer science problems. Key Topics Covered: Propositional and Predicate Logic Sets, Functions, and Relations Algorithms and Complexity Methods of Proof (Direct, Indirect, Induction, Contradiction) Combinatorics (Permutations, Combinations, Pigeonhole Principle) Graph Theory (Graphs, Trees, Connectivity, Traversal) Boolean Algebra and Logic Gates Recurrence Relations and Generating Functions Number Theory (Divisibility, Primes, Modular Arithmetic) Applications: Discrete Mathematics is fundamental to: Data Structures and Algorithms Database Theory Cryptography and Cybersecurity Network Design and Analysis Software Development and Formal Verification This course builds a strong theoretical foundation for students pursuing careers in computer science, information technology, mathematics, and engineering.